The matrix \(C_b^a\)  is referred to as the Kelmans transformation of \(C\)  from \(b\)  to \(a\)  with respect to \((t_i;s_i;k)\).
In the above setting, if \(C=(c_{ij})\)  is the adjacency matrix of an undirected graph of order \(n\)  and assume that \(C_b^a\)  is also a symmetric binary matrix, then by the assumptions in (REF )-(REF ), \(t_i=\max (0, c_{ib}-c_{ia})=\max (0, c_{bi}-c_{ai})=s_i\in \lbrace 0, 1\rbrace \)  and \(k=0\)  are uniquely determined from \(C\) . In this situation, we don't need to mention \((t_i;s_j;k)\)  and the Kelmans transformation \(C_b^a\)  of \(C\)  from \(b\)  to \(a\)  is the adjacency matrix of the graph obtained by the Kelmans transformation of an undirected graph defined by A.K. Kelmans [1]}.
